Let me say right off the bat that it seems like there is no simple solution to pairing lures and lines. Most of the time, the specifics of this are going to deal with the presentation you're aiming to cast. So, if you're looking for bass, or maybe walleye, you're going to be pairing different pieces together than you might pair heading out saltwater fishing for some more exotic specimen.
That being said, there are some key points to remember when choosing your line and lures, and choosing what goes well together.
First off, as mentioned when first talking about rods, you wanna make sure that your line and your lures match whatever rod you've chosen. You can see those specifications on the rod, as explained in this card (http://www.vingle.net/posts/328542-Choosing-a-Rod-Combining-Your-Reel-and-Rod)
Use those guidelines about weight and line thickness to guide you. Then, start to consider a few key variations:
1) What conditions will you usually be fishing?
If you're going to be fishing heavy cover, you need heavier equipment. If you'll be fishing light cover, lighter lines will get you more bites. Consider where you're going to be fishing, and if you're not sure, go for something on the heavy side of average. Why? Because lighter lines will be more affected by mismatched lures and poorly tied knots.
2) Check the lure's hook size
If it's a small (1/16 to 3/16 ounce) lure, the hook is also going to be smaller diameter, so you want to use a light weight rod and line to match this: if you go too heavy, your hooks may straighten when you try to set the hook because the rod and line will not provide the proper leverage. Similarly, if you have a heavier lure, it'll have larger hooks, and need heavier equipment to set a hook at all.
3) Retrieve Speed
Do you prefer, or plan, to keep your lure in constant motion? Or will you be letting it rest? In the first case, constant motion, you can use a heavier, visible line because the fish will focus on the lure as opposed to the line. But, if biting is slow and you'll be letting the lure sit, the fish will notice a visible line so you're going to want to go smaller with lighter lures, line and action.
Still, no matter what choice you make, you're going to have to make some compromises about your line and lure. As a beginner, though, just try some different combinations out: you'll know when you've got it right, because that's when the fish will start biting!
Next time, I'll explain more about fishing line since I realized your choice really might come back to that.